Answer with Explanation:
The relation between power and energy is
[tex]Energy=Power\times Time[/tex]
Since the nuclear reactor operates at 1200 MW throughout the year thus the energy produced in 1 year equals
[tex]E=1200\times 10^{6}\times 3600\times 24\times 365=3.784\times 10^{16}[/tex]
Now from the energy mass equivalence we have
[tex]E=mass\times c^2[/tex]
where
'c' is the speed of light in free space
Thus equating both the above values we get
[tex]3.784\times 10^{16}=mass\times (3\times 10^{8})^{2}\\\\\therefore mass=\frac{3.784\times 10^{16}}{9\times 10^{16}}=0.42kg[/tex]
Since it is given that 1 kg of mass is 34% effective thus the mass reuired for the reactor is
[tex]mass_{req}=\frac{mass}{\eta }=\frac{0.43}{0.34}=1.235[/tex]
Thus 1.235 kg of nuclear fuel is reuired for operation.
